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math.RA2025
Associative ternary algebras and ternary Lie algebras at cube roots of unity
Anti Maria Aader, Viktor Abramov, Olga Liivapuu
We propose an approach to extending the concept of a Lie algebra to ternary structures based on -symmetry, where is a primitive cube root of unity. We give a definition of a…
math.RA2015★ 1 cited
Algebras with ternary law of composition combining Z_2 and Z_3 gradings
V. Abramov, R. Kerner, O. Liivapuu
In the present article we investigate the possibility of combining the usual Grassmann algebras with their ternary Z_3-graded counterpart, thus creating a more general algebra with…
math.RA2009
Algebras with ternary law of composition and their realization by cubic matrices
V. Abramov, R. Kerner, O. Liivapuu +1
We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple…